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96                        ANALYTICAL MECHANICS
cos ei = cos 2 = 1*,   sin ei = ei,   sin 2 = Q.
Making these substitutions in the expression for/r, we obtain
/f = Umit rfo-'Q- tV.(l + *)1
i=o   L                  <                    J
where i9 is the angle r makes with the x-axis. YI
FIG. 58.
By similar reasoning we obtain the following expressions r the transverse acceleration, that is, the component of te acceleration along a perpendicular to the radius vector. * See Appendix AVI-